\contentsline {chapter}{\numberline {第一章}行列式}{1}{chapter.1}%
\contentsline {section}{\numberline {1.1}二(三)阶行列式}{1}{section.1.1}%
\contentsline {section}{\numberline {1.2}$n$阶行列式}{2}{section.1.2}%
\contentsline {section}{\numberline {1.3}行列式的展开和转置}{8}{section.1.3}%
\contentsline {section}{\numberline {1.4}行列式的计算}{13}{section.1.4}%
\contentsline {section}{\numberline {1.5}行列式的等价定义}{17}{section.1.5}%
\contentsline {section}{\numberline {1.6}Laplace定理}{20}{section.1.6}%
\contentsline {chapter}{\numberline {第二章}矩阵}{25}{chapter.2}%
\contentsline {section}{\numberline {2.1}矩阵的概念}{25}{section.2.1}%
\contentsline {section}{\numberline {2.2}矩阵的运算}{26}{section.2.2}%
\contentsline {section}{\numberline {2.3}方阵的逆阵}{30}{section.2.3}%
\contentsline {section}{\numberline {2.4}矩阵的初等变换与初等矩阵}{37}{section.2.4}%
\contentsline {section}{\numberline {2.5}分块矩阵}{44}{section.2.5}%
\contentsline {section}{\numberline {2.6}Cauchy-Binet公式}{52}{section.2.6}%
\contentsline {chapter}{\numberline {第三章}线性空间}{58}{chapter.3}%
\contentsline {section}{\numberline {3.1}数域}{58}{section.3.1}%
\contentsline {section}{\numberline {3.2}向量}{59}{section.3.2}%
\contentsline {section}{\numberline {3.3}线性空间}{60}{section.3.3}%
\contentsline {section}{\numberline {3.4}向量的线性关系}{62}{section.3.4}%
\contentsline {section}{\numberline {3.5}向量组的秩}{65}{section.3.5}%
\contentsline {section}{\numberline {3.6}矩阵的秩}{69}{section.3.6}%
\contentsline {section}{\numberline {3.7}坐标向量}{75}{section.3.7}%
\contentsline {section}{\numberline {3.8}基变换与过渡矩阵}{78}{section.3.8}%
\contentsline {section}{\numberline {3.9}子空间}{81}{section.3.9}%
\contentsline {section}{\numberline {3.10}线性方程组的解}{86}{section.3.10}%
\contentsline {chapter}{\numberline {第四章}线性映射}{95}{chapter.4}%
\contentsline {section}{\numberline {4.1}线性映射的概念}{95}{section.4.1}%
\contentsline {section}{\numberline {4.2}线性映射的运算}{98}{section.4.2}%
\contentsline {section}{\numberline {4.3}线性映射与矩阵}{101}{section.4.3}%
\contentsline {section}{\numberline {4.4}线性映射的像与核}{107}{section.4.4}%
\contentsline {section}{\numberline {4.5}不变子空间}{111}{section.4.5}%
\contentsline {chapter}{\numberline {第五章}多项式}{117}{chapter.5}%
\contentsline {section}{\numberline {5.1}一元多项式代数}{117}{section.5.1}%
\contentsline {section}{\numberline {5.2}整除}{119}{section.5.2}%
\contentsline {section}{\numberline {5.3}最大公因式}{122}{section.5.3}%
\contentsline {section}{\numberline {5.4}因式分解}{127}{section.5.4}%
\contentsline {section}{\numberline {5.5}多项式函数}{131}{section.5.5}%
\contentsline {section}{\numberline {5.6}复系数多项式}{132}{section.5.6}%
\contentsline {section}{\numberline {5.7}实系数多项式和有理系数多项式}{135}{section.5.7}%
\contentsline {section}{\numberline {5.8}多元多项式}{140}{section.5.8}%
\contentsline {section}{\numberline {5.9}对称多项式}{144}{section.5.9}%
\contentsline {section}{\numberline {5.10}结式和判别式}{148}{section.5.10}%
\contentsline {chapter}{\numberline {第六章}特征值}{155}{chapter.6}%
\contentsline {section}{\numberline {6.1}特征值和特征向量}{155}{section.6.1}%
\contentsline {section}{\numberline {6.2}对角化}{162}{section.6.2}%
\contentsline {section}{\numberline {6.3}极小多项式与 Cayley-Hamilton 定理}{167}{section.6.3}%
\contentsline {section}{\numberline {6.4}特征值的估计}{173}{section.6.4}%
\contentsline {chapter}{\numberline {第七章}相似标准型}{180}{chapter.7}%
\contentsline {section}{\numberline {7.1}多项式矩阵}{180}{section.7.1}%
\contentsline {section}{\numberline {7.2}矩阵的法式}{184}{section.7.2}%
\contentsline {section}{\numberline {7.3}不变因子}{188}{section.7.3}%
\contentsline {section}{\numberline {7.4}有理标准型}{191}{section.7.4}%
\contentsline {section}{\numberline {7.5}初等因子}{194}{section.7.5}%
\contentsline {section}{\numberline {7.6}Jordan 标准型}{196}{section.7.6}%
\contentsline {section}{\numberline {7.7}Jordan 标准型的进一步讨论和应用}{203}{section.7.7}%
\contentsline {chapter}{\numberline {第八章}二次型}{214}{chapter.8}%
\contentsline {section}{\numberline {8.1}二次型的化简与矩阵的合同}{214}{section.8.1}%
\contentsline {section}{\numberline {8.2}二次型的化简}{218}{section.8.2}%
\contentsline {section}{\numberline {8.3}惯性定理}{222}{section.8.3}%
\contentsline {section}{\numberline {8.4}正定型与正定矩阵}{224}{section.8.4}%
\contentsline {section}{\numberline {8.5}Hermite型}{231}{section.8.5}%
\contentsline {chapter}{\numberline {第九章}内积空间}{235}{chapter.9}%
\contentsline {section}{\numberline {9.1}内积空间的概念}{235}{section.9.1}%
\contentsline {section}{\numberline {9.2}内积的表示和正交基}{239}{section.9.2}%
\contentsline {section}{\numberline {9.3}伴随}{244}{section.9.3}%
\contentsline {section}{\numberline {9.4}内积空间的同构, 正交变换和酉变换}{247}{section.9.4}%
\contentsline {section}{\numberline {9.5}自伴随算子}{252}{section.9.5}%
\contentsline {section}{\numberline {9.6} 正规算子}{257}{section.9.6}%
\contentsline {section}{\numberline {9.7}实正规矩阵}{260}{section.9.7}%
\contentsline {section}{\numberline {9.8}谱}{266}{section.9.8}%
\contentsline {section}{\numberline {9.9}奇异值分解}{270}{section.9.9}%
\contentsline {chapter}{\numberline {第十章}一些有趣的例题}{275}{chapter.10}%
\contentsline {chapter}{\numberline {第十一章}版本更新历史}{278}{chapter.11}%
\contentsline {chapter}{参考文献}{279}{chapter*.8}%
\renewcommand {\cftchappresnum }{附录 }\renewcommand {\cftchapaftersnum }{}
\contentsline {chapter}{\numberline {A}基本数学工具}{280}{appendix.A}%
\contentsline {section}{\numberline {A.1}求和算子与描述统计量}{280}{section.A.1}%
